Question

cos²a + cos²a cot²a = cot²a

Answer 1

This problem has no solution. Because if we simplify it we get cos2A = -3 which is not possible for any value of A as -1<=cos@<=1

Answer 2

${ \cos(x) }^{2} + { \cos(x) }^{2} { \cot(x) }^{2} \\ = { \cos(x) }^{2} + \frac{ { \cos(x) }^{2} { \cos(x) }^{2} }{ { \sin(x) }^{2} } \\ = \frac{ { \cos(x ) }^{2} { \sin(x) }^{2} + { \cos(x) }^{2} { \cos(x) }^{2} }{ { \sin(x) }^{2} } \\ = \frac{ { \cos(x) }^{2} ( { \sin(x) }^{2} + { \cos(x) }^{2}) }{ { \sin(x) }^{2} }$
Como sen²(x) + cos²(x)=1
$= \frac{ { \cos(x) }^{2} }{ { \sin(x) }^{2} } = { \cot(x) }^{2}$